Orthogonal frequency division multiplexing (OFDM) is a multicarrier modulation technique that employs orthogonal subcarriers. OFDM systems can be implemented efficiently by means of inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) at the transmitter and receiver, respectively. Bandwidth efficiency and immunity to multipath propagation are the main advantages of OFDM over single carrier transmission [1]. Consequently, OFDM has been adopted in many wireless digital communication standards such as digital video broadcasting-terrestrial (DVB-T) [2], Interoperability for Microwave Access (WiMAX) technologies [3], the Long Term Evolution LTE-Advanced (LTE-A) [4]. For wired systems, OFDM has been adopted for broadband communications over powerline communications [5]. Moreover, OFDM is a strong candidate for the upcoming fifth generation (5G) wireless communications standard [6].
The knowledge of the channel state information (CSI), commonly known as channel estimation, and equalization are fundamental tasks that a receiver has to perform prior to the information symbols extraction from the received signal. The accuracy of the CSI is one of the key factors that determine the error performance of communications systems [7]. Consequently, channel estimation has to be performed meticulously to avoid increasing the system error rate. Consequently, channel estimation for OFDM has attracted remarkable attention in the literature. Generally speaking, the channel estimation techniques reported in the literature can be classified based on their accuracy, spectral efficiency, computational complexity, or observation window size. Typically, the objective in most of the work reported in the literature is to maximize the accuracy and spectral efficiency, while minimizing the complexity and observation window size. However, these are conflicting objectives and hence, it is difficult to achieve all of them simultaneously.
Based on their spectral efficiency, channel estimation techniques are typically classified as blind [8]-[13], or pilot-aided [14]-[18]. However, such classification can be misleading in various scenarios. For example, certain channel estimation algorithms are considered as blind while they have constraints on the modulation type [8]-[11], and hence, their spectral efficiency could actually be worse than pilot-aided techniques under bit error rate (BER) and data rate constraints. Therefore, an accurate and more informative metric is needed to evaluate and compare the spectral efficiency of various channel estimation algorithms. Moreover, it would be more factual to denote modulation-type constrained blind techniques as conditionally-blind. In practical OFDM systems such as LTE-A [4], comb-type pilots are deployed in the time-frequency subcarrier grid as shown in FIG. 1. Such structure implies that 4.7% of the system bandwidth is wasted for pilots. The bandwidth efficiency can be even lower for some other systems such as the IEEE 802.11n where pilot symbols constitutes 7.1% of the system bandwidth. Moreover, in particular communications systems such burst transmission, frequency hopping and cognitive radio, the channel responses over two consecutive OFDM symbols could be uncorrelated, and hence, pilot symbols are needed in every OFDM symbol which would degrade the spectrum efficiency drastically.
Computational complexity is another major metric used to compare various channel estimation techniques. Generally speaking, blind estimation techniques have higher computational complexity [13] than pilot-aided techniques [7]. The excessive computational complexity is mainly caused by the iterative structure of the algorithm [13]-[15], or due to the requirements of performing extensive search over the solution space [12]. Although the complexity of the system reported in [12] becomes comparable to pilot-aided estimation at high signal-to-noise ratios (SNR), such condition can be frequently violated in practical scenarios. It is worth noting that there is no unified threshold that can be used to classify channel estimation algorithms based on their complexity. Nevertheless, low computational complexity is typically claimed when the total number of mathematical operations is a linear function of the system and channel parameters [12]. Alternatively, low complexity is claimed when a particular system computational complexity is low compared to other well established estimators [17], [18].
The observation window size specifies the number of symbols required to obtain the CSI. In such systems, the channel is assumed to be fixed over the observation period [8], [9], [11], [13]. While such assumption might be suitable for static and slow fading channels, definitely it will not be the case in mobile channels. Moreover, if the observation window size is large, such assumption becomes suitable only for static channels. Channel estimators that can perform the CSI within one OFDM period, denoted as one-shot estimators, may usually provide better performance as compared to other estimators with multiple-symbols observation window [12].
As it can be noted from the aforementioned discussion, pilot-aided estimators have several desired features in terms of complexity and estimation accuracy. However, the spectral efficiency remains as the major concern. Practically speaking, prominent standards such as DVB-T [2], [3] WiMAX and LTE-A [4] are using pilot symbols, which implies that systems' designers prefer to sacrifice the spectral efficiency for other desired features such as low complexity, robustness and freedom of choosing the modulation type. Despite the large number of articles that tackle the channel estimation problem, to the best of our knowledge, there is no technique available yet that offers all the aforementioned desired features simultaneously.